A system for fastening a rail to a solid foundation, and a method for renovating a rail-fastening point. The system and the method allow a fastening point for a rail to be easily and economically renovated in such a way that a permanently reliable function of the renovated fastening is then ensured again while the worn support section remains. The system for fastening a rail to a solid ground foundation includes: a layer formed by a compensating mass applied to the support section; a base plate resting on the layer and extending over the support section, upon which the rail is supported in the finally installed state; a spring element for exerting a resilient elastic retention force on the rail; and a clamping element that can be anchored in the solid foundation for clamping the spring element.